BENDIER: Bayesian Estimation of Nonlinear Deformation: Inference for Elastic Robots

Description

Continuum robot state estimation can be formulated similarly to SLAM, where variables are connected through spatial motion priors and measurement factors. This repository demonstrates how to construct factor graph representations of the conditional distribution over continuum robot configurations.

We leverage the sparse nonlinear optimization capabilities of GTSAM to efficiently estimate continuum robot states. The repository supports:

• bendier_solvers: A standalone static C++ library implementing factor graph optimization methods
• bendier: Python package that bundles solver bindings and plotters under one import

If you use this code, please cite our RAL paper (see preprint version here):

@article{ferguson2026continuum,
  title   = {Continuum Robot State Estimation with Actuation Uncertainty},
  author  = {Ferguson, James M. and Kuntz, Alan and Hermans, Tucker},
  journal = {IEEE Robotics and Automation Letters},
  volume  = {xx},
  number  = {x},
  pages   = {xxx--xxx},
  year    = {2026},
  doi     = {xxxxxxxxxxx}
}

TODO: Add citation metadata once the paper is published.

Build/Install Dependencies

Install Eigen3

Eigen3 is required for numerical linear algebra operations in bendier and gtsam. You likely already have it installed, but if not, you can install with:

sudo apt update
sudo apt install -y libeigen3-dev

We have tested with Eigen3 version: 3.4.0.

Build/Install GTSAM

bendier dynamically loads classes from GTSAM, so GTSAM must first be built and installed. The best way to do this is from source, which allows you to ensure that all required dependencies are properly configured.

First clone GTSAM and create a build directory:

git clone https://github.com/borglab/gtsam.git
cd gtsam
git checkout 4.3a1 # Tested GTSAM version
mkdir build 
cd build

Next configure the build with CMake:

cmake .. -DGTSAM_USE_SYSTEM_EIGEN=ON

Use system Eigen for GTSAM (-DGTSAM_USE_SYSTEM_EIGEN=ON) so both GTSAM and bendier resolve Eigen from the same system installation. This avoids accidentally mixing GTSAM's internal vendored Eigen headers with the system Eigen headers.

At this point, verify that CMake found all required dependencies (e.g., Boost, Eigen, TBB). Ensure that there are no critical warnings during configuration. For more information on dependencies, see the GTSAM installation documentation

If everything looks good, you can now build and install gtsam, which will take several minutes:

make -j8
sudo make install

This installs GTSAM headers (needed to build bendier) in /usr/local/include and library files (needed to run bendier) in /usr/local/lib.

Build/Install bendier python package

First clone this repository:

git clone https://github.com/Kuntz-Lab/bendier.git
cd bendier

Next create and activate a Python virtual environment:

python3 -m venv .venv
source .venv/bin/activate

Note that we have tested with Python 3.12.3 but expect that other versions should work as well.

Install the python dependencies required for plotting and simulation:

pip install -r requirements.txt

Now build and install the bendier Python package:

pip install . -v

The final output should include Successfully installed bendier, meaning that you can now import bendier in Python when the virtual environment is active.

Build C++ library Only

cmake -S . -B build-cpp -DBENDIER_BUILD_PYTHON=OFF
cmake --build build-cpp -j
cmake --install build-cpp --prefix build-cpp/install

This produces a standalone bendier_solvers C++ library. The last line creates a staged install under build-cpp/install/ that you can copy or point other projects at.

Run Test Scripts

Plotting utilities live in the bendier.plotting package, and runnable examples/tests live in python/tests/. There are several examples you can run to verify the solvers are working. Here are a few options:

cd python

python -m tests.cosserat.test_priors_sim
python -m tests.cosserat.spring_sim
python -m tests.tendon_robot.test_simple
python -m tests.parallel_robot.test_simple

All RAL paper simulations can be run with

bash run_sims.bash

When the chosen script runs successfully, a PyVista render window will appear showing real-time solution geometries for the selected model. Solution metadata is displayed in the upper-right corner, including optimization solve times and related diagnostics.

Debugging Tips

1. You may get something like: ImportError: libgtsam.so.4: cannot open shared object file: No such file or directory. This indicates that the GTSAM library installation directory is not visible to the dynamic linker. In most cases this can be resolved by running sudo ldconfig and then rerunning the script.

2. If plotting is slow, first check which GPU is actually rendering OpenGL. On Ubuntu this is usually the most useful single command:

glxinfo -B

Look for OpenGL vendor string and OpenGL renderer string:

• llvmpipe, softpipe, or OSMesa means software rendering.
• Intel means the integrated GPU is active.
• NVIDIA means the discrete NVIDIA GPU is active.

To switch the machine to NVIDIA system-wide (careful!), use PRIME Select and reboot:

sudo prime-select nvidia
sudo reboot

If you do not want to change the whole session, you can run like this to select the GPU on a per-command basis:

__NV_PRIME_RENDER_OFFLOAD=1 __GLX_VENDOR_LIBRARY_NAME=nvidia python -m tests.parallel_robot.test_simple